Found on the flip of the 20 th century, p-adic numbers are usually utilized by mathematicians and physicists. this article is a self-contained presentation of simple p-adic research with a spotlight on analytic themes. It bargains many positive factors hardly ever handled in introductory p-adic texts reminiscent of topological versions of p-adic areas inside of Euclidian house, a distinct case of Hazewinkel’s sensible equation lemma, and a therapy of analytic components.

Elliptic stories describes the most recent advancements in quantity idea by means of taking a look at essentially the most intriguing unsolved difficulties in modern mathematics—the Birch and Swinnerton-Dyer Conjecture. during this ebook, Avner Ash and Robert Gross advisor readers throughout the arithmetic they should comprehend this fascinating challenge.

An innovative advent to quantity conception, this special approach employs a couple of fictional characters, Ant and Gnam. Ant leads Gnam via a number of theories, and jointly, they positioned the theories into action—applying linear diophantine equations to soccer scoring, utilizing a black-magic equipment to simplify difficulties in modular buildings, and constructing exciting ameliorations to the foundations of chess.